SAN BENITO, Texas (CNN) -- Two U.S. Border Patrol agents were shot to death and a third was critically wounded during a car chase on Tuesday, police said.

One of the suspects also was shot and wounded. The other got away.

The federal agents who were killed were a man and woman whose identities were not immediately disclosed. The third agent who was shot was taken to a hospital in nearby Harlingen, Texas, in critical condition. The wounded suspect was taken to the same hospital.

The incident started with the report of a shooting just outside this Mexican border community that was investigated by the Cameron County Sheriff's Department.

There were no details of the first shooting, which was reported to San Benito Police at 5:20 a.m.

Deputies pursued a vehicle thought to contain the shooting suspects, but lost it between San Benito and Harlingen and put out a bulletin, according to Officer Albert Aguirre of the San Benito Police Department.

Border Patrol agents spotted the car, gave chase and managed to stop it, but a shootout erupted and three agents were shot.

The suspects took off again and sheriff's department officers chased them through San Benito where one of the suspects was shot, wounded and captured.

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